true/false. write 't' if the statement is true and 'f' if ......9) _____ 10) the...

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

1) Subjective probability implies that we can measure the relative frequency of the values of the

random variable.

1) _______

2) The use of "expert opinion" is one way to approximate subjective probability values. 2) _______

3) Mutually exclusive events exist if only one of the events can occur on any one trial. 3) _______

4) Stating that two events are statistically independent means that the probability of one event

occurring is independent of the probability of the other event having occurred.

4) _______

5) Saying that a set of events is collectively exhaustive implies that one of the events must occur. 5) _______

6) Saying that a set of events is mutually exclusive and collectively exhaustive implies that one and

only one of the events can occur on any trial.

6) _______

7) A posterior probability is a revised probability. 7) _______

8) Bayes' theorem enables us to calculate the probability that one event takes place knowing that a

second event has or has not taken place.

8) _______

9) A probability density function is a mathematical way of describing Bayes' theorem. 9) _______

10) The probability, P, of any event or state of nature occurring is greater than or equal to 0 and less

than or equal to 1.

10) ______

11) A probability is a numerical statement about the chance that an event will occur. 11) ______

12) If two events are mutually exclusive, the probability of both events occurring is simply the sum

of the individual probabilities.

12) ______

13) Given two statistically dependent events (A,B), the conditional probability of P(A|B) =

P(B)/P(AB).

13) ______

14) Given two statistically independent events (A,B), the joint probability of P(AB) = P(A) + P(B). 14) ______

15) Given three statistically independent events (A,B,C), the joint probability of P(ABC) = P(A) × P(B)

× P(C).

15) ______

16) Given two statistically independent events (A,B), the conditional probability P(A|B) = P(A). 16) ______

17) Suppose that you enter a drawing by obtaining one of 20 tickets that have been distributed. By

using the classical method, you can determine that the probability of your winning the drawing is

0.05.

17) ______

18) Assume that you have a box containing five balls: two red and three white. You draw a ball

two times, each time replacing the ball just drawn before drawing the next. The probability of

drawing only one white ball is 0.20.

18) ______

19) If we roll a single die twice, the probability that the sum of the dots showing on the two rolls

equals four (4), is 1/6.

19) ______

20) For two events A and B that are not mutually exclusive, the probability that either A or B will

occur is P(A) × P(B) - P(A and B).

20) ______

21) If we flip a coin three times, the probability of getting three heads is 0.125. 21) ______

22) Consider a standard 52-card deck of cards. The probability of drawing either a seven or a black

card is 7/13.

22) ______

23) If a bucket has three black balls and seven green balls, and we draw balls without replacement,

the probability of drawing a green ball is independent of the number of balls previously drawn.

23) ______

24) Assume that you have an urn containing 10 balls of the following description:

4 are white (W) and lettered (L)

2 are white (W) and numbered (N)

3 are yellow (Y) and lettered (L)

1 is yellow (Y) and numbered (N)

If you draw a numbered ball (N), the probability that this ball is white (W) is 0.667.

24) ______






If you draw a numbered ball (N), the probability that this ball is white (W) is 0.60.

25) ______






If you draw a lettered ball (L), the probability that this ball is white (W) is 0.571.

26) ______

27) The joint probability of two or more independent events occurring is the sum of their marginal

or simple probabilities.

27) ______

28) The number of bad checks written at a local store is an example of a discrete random variable. 28) ______

29) Given the following distribution:

Outcome

Value of

Random Variable Probability

A 1 .4

B 2 .3

C 3 .2

D 4 .1

The expected value is 3.

29) ______

30) A new young executive is perplexed at the number of interruptions that occur due to employee rela tions.

She has

decided

to track

the

number

of

interrupt

ions that

occur

during

each

hour of

her day.

Over the

last

month,

she has

determin

ed that

between

0 and 3

interrupt

ions

occur

during

any

given

hour of

her day.

The data

is shown

below.

Number of Interruptions in 1 hour Probability

0 interruption .5

1 interruptions .3

2 interruptions .1

3 interruptions .1

On

average,

she

should

expect

0.8

interrupt

ions per

hour.

30) ___

___

31) A new young executive is perplexed at the number of interruptions that occur due to employee

relations. She has decided to track the number of interruptions that occur during each hour of

her day. Over the last month, she has determined that between 0 and 3 interruptions occur

dur

ing

any

given

hour of

her

day. The

data is

shown

below.

Number of Interruptions in 1 hour Probability

0 interruption .4

1 interruptions .3

2 interruptions .2

3 interruptions .1

On

average,

she

should

expect

1.0

interrupt

ions per

hour.

31) ___

___

32) The expected value of a binomial distribution is expressed as np, where n equals the number of

trials and p equals the probability of success of any individual trial.

32) ______

33) The standard deviation equals the square of the variance. 33) ______

34) The probability of obtaining specific outcomes in a Bernoulli process is described by the

binomial probability distribution.

34) ______

35) The variance of a binomial distribution is expressed as np/(1-p), where n equals the number of

trials and p equals the probability of success of any individual trial.

35) ______

36) The F distribution is a continuous probability distribution that is helpful in testing hypotheses

about variances.

36) ______

37) The mean and standard deviation of the Poisson distribution are equal. 37) ______

38) In a normal distribution the Z value represents the number of standard deviations from a value

X to the mean.

38) ______

39) Assume you have a normal distribution representing the likelihood of completion times. The

mean of this distribution is 10, and the standard deviation is 3. The probability of completing

the project in 8 or fewer days is the same as the probability of completing the project in 18 days

or more.

39) ______

40) Assume you have a normal distribution representing the likelihood of completion times. The

mean of this distribution is 10, and the standard deviation is 3. The probability of completing

the project in 7 or fewer days is the same as the probability of completing the project in 13 days

or more.

40) ______

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

41) The classical method of determining probability is 41) ______

A) marginal probability.

B) objective probability.

C) subjective probability.

D) joint probability.

E) conditional probability.

42) Subjective probability assessments depend on 42) ______

A) experience and judgment.

B) the number of occurrences of the event.

C) the relative frequency of occurrence.

D) the total number of trials.

E) None of the above

43) If two events are mutually exclusive, then 43) ______

A) their probabilities can be added.

B) if one occurs, the other cannot occur.

C) they may also be collectively exhaustive.

D) the joint probability is equal to 0.

E) All of the above

44) A ________ is a numerical statement about the likelihood that an event will occur. 44) ______

A) standard deviation

B) collectively exhaustive construct

C) probability

D) mutually exclusive construct

E) variance

45) A conditional probability P(B|A) is equal to its marginal probability P(B) if 45) ______

A) the events are mutually exclusive.

B) it is a joint probability.

C) P(A) = P(B).

D) statistical dependence exists.

E) statistical independence exists.

46) The equation P(A|B) = P(AB)/P(B) is 46) ______

A) the formula for a joint probability.

B) the marginal probability.

C) the formula for a conditional probability.

D) only relevant when events A and B are collectively exhaustive.


47) Suppose that we determine the probability of a warm winter based on the number of warm

winters experienced over the past 10 years. In this case, we have used ________.

47) ______

A) subjective probability

B) relative frequency

C) the classical method

D) the logical method


48) Bayes' theorem is used to calculate 48) ______

A) subjective probabilities.

B) joint probabilities.

C) marginal probabilities.

D) revised probabilities.

E) prior probabilities.

49) If the sale of ice cream and pizza are independent, then as ice cream sales decrease by 60 percent

during the winter months, pizza sales will

49) ______

A) decrease by 60 percent.

B) increase by 40 percent.

C) increase by 60 percent.

D) decrease by 40 percent.

E) be unrelated.

50) If P(A) = 0.3, P(B) = 0.2, P(A and B) = 0.0 , what can be said about events A and B? 50) ______

A) They are mutually exclusive.

B) They are independent.

C) They are posterior probabilities.

D) None of the above

E) All of the above

51) Suppose that 10 golfers enter a tournament and that their respective skill levels are

approximately the same. What is the probability that one of the first three golfers that

registered for the tournament will win?

51) ______

A) 0.100 B) 0.001 C) 0.299 D) 0.700 E) 0.300


approximately the same. Six of the entrants are female and two of those are older than 40 years

old. Three of the men are older than 40 years old. What is the probability that the winner will

be either female or older than 40 years old?

52) ______

A) 0.198 B) 0.900 C) 1.100 D) 0.200 E) 0.000


approximately the same. Six of the entrants are female and two of those are older than 40 years

old. Three of the men are older than 40 years old. What is the probability that the winner will

be a female who is older than 40 years old?

53) ______

A) 1.100 B) 0.000 C) 0.198 D) 0.200 E) 0.900

54) "The probability of event B, given that event A has occurred" is known as a ________ probability. 54) ______

A) marginal

B) continuous

C) conditional

D) joint

E) simple

55) When does P(A|B) = P(A)? 55) ______

A) when A and B are mutually exclusive

B) when A and B are statistically dependent

C) when A and B are statistically independent

D) when P(B) = 0

E) when A and B are collectively exhaustive

56) A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the

firm is randomly selecting two different employee names to "win" the tickets. There are 6

secr

etar

ies, 5

consult

ants and

4

partners

in the

firm.

Which of

the

followin

g

statemen

ts is not

true?

56) ___

___

A) The probability of a secretary winning a ticket on the first draw is 6/15.

B) The probability of two secretaries winning both tickets is 1/7.

C) The probability of a secretary winning a ticket on the second draw given that a consultant

won a ticket on the first draw is 6/15.

D) The probability of a partner winning a ticket on the second draw given that a secretary won

a ticket on the first draw is 4/14.

E) The probability of a consultant winning a ticket on the first draw is 1/3.



secretaries, 5 consultants, and 4 partners in the firm. Which of the following statements is true?

57) ______

A) The probability of a consultant winning on the second draw given that a consultant won on

the first draw is 5/14.

B) The probability of a partner winning on the second draw given that a secretary won on the

first draw is 8/30.

C) The probability of a partner winning on the second draw given that a partner won on the

first draw is 3/14.

D) The probability of a secretary winning on the second draw given that a secretary won on

the first draw is 2/15.

E) None of the above are true.



secretaries, 5 consultants, and 4 partners in the firm. Which of the following statements is true?

58) ______

A) The probability of two secretaries winning is the same as the probability of a secretary

winning on the second draw given that a consultant won on the first draw.

B) The probability of a secretary winning on the second draw given that a consultant won on

the first draw is the same as the probability of a consultant winning on the second draw

given that a secretary won on the first draw.

C) The probability that both tickets will be won by partners is the same as the probability that

a consultant and secretary will win.

D) The probability of a secretary and a consultant winning is the same as the probability of a

secretary and secretary winning.

E) None of the above are true.

59) At a university with 1,000 business majors, there are 200 business students enrolled in an

introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory

accounting course. There are an additional 250 business students enrolled in accounting but not

enrolled in statistics. If a business student is selected at random, what is the probability that the

student is either enrolled in accounting or statistics, but not both?

59) ______

A) 0.50

B) 0.45

C) 0.40

D) 0.05






student is enrolled in accounting?

60) ______

A) 0.50

B) 0.20

C) 0.25

D) 0.30






student is enrolled in statistics?

61) ______

A) 0.30

B) 0.20

C) 0.05

D) 0.25






student is enrolled in both statistics and accounting?

62) ______

A) 0.25

B) 0.05

C) 0.06

D) 0.20





enrolled in statistics. If a business student is selected at random and found to be enrolled in

statistics, what is the probability that the student is also enrolled in accounting?

63) ______

A) 0.30

B) 0.25

C) 0.05

D) 0.20


64) Suppose that when the temperature is between 35 and 50 degrees, it has historically rained 40%

of the time. Also, historically, the month of April has had a temperature between 35 and 50

deg

rees

on 25

days.

You have

schedule

d a golf

tournam

ent for

April 12.

What is

the

probabili

ty that

players

will

experien

ce rain

and a

temperat

ure

between

35 and 50

degrees?

64) ___

___

A) 0.333 B) 0.400 C) 0.480 D) 1.000 E) 0.833

65) Suppose that, historically, April has experienced rain and a temperature between 35 and 50

degrees on 20 days. Also, historically, the month of April has had a temperature between 35

and 50 degrees on 25 days. You have scheduled a golf tournament for April 12. If the

temperature is between 35 and 50 degrees on that day, what will be the probability that the

players will get wet?

65) ______

A) 0.556 B) 0.333 C) 0.800 D) 0.667 E) 1.000


introductory statistics course. Of these 200, 50 are also enrolled in an introductory accounting

course. There are an additional 250 business students enrolled in accounting but not enrolled in

statistics. If a business student is selected at random, what is the probability that the student is

enrolled in neither accounting nor statistics?

66) ______

A) 0.55

B) 0.45

C) 0.05

D) 0.50



introductory statistics course. Of these 200, 50 are also enrolled in an introductory accounting

course. There are an additional 250 business students enrolled in accounting but not enrolled in

statistics. If a business student is selected at random, what is the probability that the student is

not enrolled in accounting?

67) ______

A) 0.50

B) 0.25

C) 0.30

D) 0.20


68) At a university with 1,000 business majors, there are 200 business students enrolled in an intr oductor

y

statistics

course.

Of these

200, 50

are also

enrolled

in an

introduct

ory

accounti

ng

course.

There are

an

addition

al 250

business

students

enrolled

in

accounti

ng but

not

enrolled

in

statistics.

If a

business

student

is

selected

at

random,

what is

the

probabili

ty that

the

student

is not

enrolled

in

statistics

?

68) ___

___

A) 0.80

B) 0.05

C) 0.20

D) 0.25


69) A production process is known to produce a particular item in such a way that 5 percent of these are defecti

ve. If two

items are

randoml

y

selected

as they

come off

the

producti

on line,

what is

the

probabili

ty that

the

second

item will

be

defective

?

69) ___

___

A) 0.20

B) 0.18

C) 0.005

D) 0.05


70) A production process is known to produce a particular item in such a way that 5 percent of these

are defective. If two items are randomly selected as they come off the production line, what is

the probability that both are defective (assuming that they are independent)?

70) ______

A) 0.0025 B) 0.0100 C) 0.0250 D) 0.1000 E) 0.2000

71) A company is considering producing some new Gameboy electronic games. Based on past

records, management believes that there is a 70 percent chance that each of these will be

successful and a 30 percent chance of failure. Market research may be used to revise these

probabilities. In the past, the successful products were predicted to be successful based on

market research 90 percent of the time. However, for products that failed, the market research

predicted these would be successes 20 percent of the time. If market research is performed for a

new product, what is the probability that the results indicate a successful market for the product

and the product is actually not successful?

71) ______

A) 0.06 B) 0.27 C) 0.07 D) 0.24 E) 0.63







new product, what is the probability that the results indicate an unsuccessful market for the

product and the product is actually successful?

72) ______

A) 0.63 B) 0.06 C) 0.21 D) 0.07 E) 0.24

73) A company is considering producing some new Gameboy electronic games. Based on past records,

manage

ment

believes

that

there is a

70

percent

chance

that each

of these

will be

successfu

l and a

30

percent

chance of

failure.

Market

research

may be

used to

revise

these

probabili

ties. In

the past,

the

successfu

l

products

were

predicte

d to be

successfu

l based

on

market

research

90

percent

of the

time.

However

, for

products

that

failed,

the

market

research

predicte

d these

would be successes 20 percent of the time. If market research is performed for a new product,

what is the probability that the results indicate an unsuccessful market for the product and the

product is actually unsuccessful?

73) ______

A) 0.07 B) 0.63 C) 0.21 D) 0.24 E) 0.06



successful, and a 30 percent chance of failure. Market research may be used to revise these




new product, what is the probability that the product will be successful if the market research

indicates a success?

74) ______

A) 0.10 B) 0.09 C) 0.91 D) 0.63 E) 0.90

75) A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge.

Management believes 60 percent of customers will take advantage of this service. They are also

considering offering customers the option of opening an account and receiving monthly bills.

They believe 60 percent of their customers (regardless of whether or not they use the pick-up

service) will use the account service. If the two services are introduced to the market, what is the

probability a customer uses both services?

75) ______

A) 0.36

B) 0.24

C) 0.60

D) 0.12



Management believes 60 percent of the existing customers will take advantage of this service.

They are also considering offering customers the option of opening an account and receiving

monthly bills. They believe 60 percent of customers (regardless of whether or not they use the

pick-up service) will use the account service. If the two services are introduced to the market,

what is the probability that a customer uses only one of these services?

76) ______

A) 0.24

B) 0.60

C) 0.40

D) 0.48



Management believes 60 percent of the existing customers will take advantage of this service.

They are also considering offering customers the option of opening an account and receiving

monthly bills. They believe 60 percent of customers (regardless of whether or not they use the

pick-up service) will use the account service. If the two services are introduced to the market,

what is the probability a customer uses neither of these services?

77) ______

A) 0.24

B) 0.36

C) 0.80

D) 0.16






mar

ket

rese

arc

h 90

percent

of the

time.

However

, for

products

that

failed,

the

market

research

predicte

d these

would be

successes

20

percent

of the

time. If

market

research

is

performe

d for a

new

product,

what is

the

probabili

ty that

the

product

will be

successfu

l if the

market

research

indicates

a failure?

78) ___

___

A) 0.20 B) 0.91 C) 0.90 D) 0.23 E) 0.63

79) Which distribution is helpful in testing hypotheses about variances? 79) ______

A) normal distribution

B) F distribution

C) exponential distribution

D) Poisson distribution

E) binomial distribution

80) A company is considering producing two new electronic games designed for the popular

Gameboy toy. Based on market data, management believes there is a 60 percent chance that a

"cops and robbers" game will be successful and a 40 percent chance that a "let's play house"

game will be successful. As these products are completely different, it may be assumed that the

success of one is totally independent of the success of the other. If two products are introduced

to the market, what is the probability that both are successful?

80) ______

A) 0.24

B) 0.12

C) 0.36

D) 0.60


81) A company is considering producing two new electronic games designed for the popular

Gameboy toy. Based on market data, management believes that there is a 60 percent chance

that a "cops and robbers" game will be successful and a 40 percent chance that "let's play house"

game will be successful. As these products are completely different, it may be assumed that the

success of one is totally independent of the success of the other. If two products are introduced

to the market, what is the probability that both are failures?

81) ______

A) 0.36

B) 0.80

C) 0.24

D) 0.16








new product, what is the probability that the results indicate a successful market for the product

and the product actually is successful?

82) ______

A) 0.54

B) 0.63

C) 0.60

D) 0.90


83) The expected value of a probability distribution is 83) ______

A) the variance of the distribution.

B) the probability density function.

C) the range of continuous values from point A to point B, inclusive.

D) the measure of the spread of the distribution.

E) the average value of the distribution.

84) Which of the following is not true for discrete random variables? 84) ______

A) A binomial random variable is considered discrete.

B) The expected value is the weighted average of the values.

C) They can assume only a countable number of values.

D) The probability values always sum up to 1.

E) The probability of each value of the random variable must be 0.

85) The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1,

or 2. The probabilities are the same for each of these (1/3). If X is the number of calls arriving in

a five-minute time period, what is the mean of X?

85) ______

A) 4/3

B) 2/3

C) 1/3

D) 1


86) The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1,

2, 3, 4, 5, or 6. The probabilities are the same for each of these (1/7). If X is the number of calls

arriving in a five-minute time period, what is the mean of X?

86) ______

A) 3

B) 4

C) 5

D) 2


87) A discrete random variable has a mean of 400 and a variance of 64. What is the standard

deviation?

87) ______

A) 8

B) 20

C) 64

D) 400


88) Which of the following is not true about continuous random variables? 88) ______

A) The area under each of the curves represents probabilities.

B) They can only be integer values.

C) The entire area under each of the curves equals 1.

D) They have an infinite set of values.

E) Some may be described by uniform distributions or exponential distributions.

89) Historical data indicates that only 20% of cable customers are willing to switch companies. If a

binomial process is assumed, then in a sample of 20 cable customers, what is the probability that

exactly 2 customers would be willing to switch their cable?

89) ______

A) 0.1 B) 0.04 C) 0.794 D) 0.206 E) 0.137

90) Historical data indicates that only 20% of cable customers are willing to switch companies. If a

binomial process is assumed, then in a sample of 20 cable customers, what is the probability that

no more than 3 customers would be willing to switch their cable?

90) ______

A) 0.20 B) 0.411 C) 0.15 D) 0.589 E) 0.85

91) Properties of the normal distribution include 91) ______

A) use in queuing.

B) a discrete probability distribution.

C) a continuous bell-shaped distribution.

D) the number of trials is known and is either 1, 2, 3, 4, 5, etc.

E) the random variable can assume only a finite or limited set of values.

92) Which of the following characteristics is true for a normal probability distribution? 92) ______

A) It is symmetrical.

B) The area under the curve is 1.

C) The midpoint is also the mean.

D) Sixty-eight percent of the area under the curve lies within one standard deviation of the

mean.

E) All of the above are true.

93) The number of cell phone minutes used by high school seniors follows a normal distribution wit h a

mean of

500 and a

standard

deviation

of 50.

What is

the

probabili

ty that a

student

uses

fewer

than 600

minutes?

93) ___

___

A) 0.023

B) 0

C) 0.841

D) 0.977


94) The number of cell phone minutes used by high school seniors follows a normal distribution

with a mean of 500 and a standard deviation of 50. What is the probability that a student uses

fewer than 400 minutes?

94) ______

A) 0.159

B) 0

C) 0.023

D) 0.977




more than 350 minutes?

95) ______

A) 0.999

B) 0.618

C) 0.001

D) 0.382




more than 580 minutes?

96) ______

A) 0.0548

B) 0.848

C) 0.903

D) 0.152


97) Data for a particular subdivision near downtown Houston indicate that the average price per

square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is

the probability that the average price per square foot for a home is greater than $110?

97) ______

A) 0.977

B) 0

C) 0.841

D) 0.023




the probability that the average price per square foot for a home is greater than $90?

98) ______

A) 0.159

B) 0.977

C) 0.023

D) 0




the probability that the average price per square foot for a home is less than $85?

99) ______

A) 0.999

B) 0.618

C) 0.382

D) 0.001




the probability that the average price per square foot for a home is less than $108?

100) _____

A) 0.152

B) 0.848

C) 0.945

D) 0.097


101) The time required to complete a project is normally distributed with a mean of 80 weeks and a

standard deviation of 10 weeks. The construction company must pay a penalty if the project is

not finished by the due date in the contract. If a construction company bidding on this contract

puts in a due date of 80 weeks, what is the probability that they will have to pay a penalty?

101) _____

A) 0.500

B) 1/8

C) 1.000

D) 0


102) The time required to complete a project is normally distributed with a mean of 80 weeks and a

standard deviation of 10 weeks. The construction company must pay a penalty if the project is

not finished by the due date in the contract. If a construction company bidding on this contract

wishes to be 90 percent sure of finishing by the due date, what due date (project week #) should

be negotiated?

102) _____

A) 81.28

B) .81954

C) 92.8

D) 81.82


103) The time required to travel downtown at 10 a.m. on Monday morning is known to be normally

distributed with a mean of 40 minutes and a standard deviation of 5 minutes. What is the

probability that it will take less than 40 minutes?

103) _____

A) 1.00

B) 0.80

C) 0.20

D) 0.50




probability that it will take less than 35 minutes?

104) _____

A) 0.53983

B) 0.15866

C) 0.46017

D) 0.84134




probability that it will take more than 40 minutes?

105) _____

A) 0.0625

B) 0.5000

C) 0.2500

D) 1.000


106) Queuing Theory makes use of the 106) _____

A) uniform probability distribution.

B) binomial probability distribution.

C) Poisson probability distribution.

D) normal probability distribution.


107) The number of cars passing through an intersection in the next five minutes can usually be

described by the

107) _____

A) exponential distribution.

B) Poisson distribution.

C) normal distribution.

D) uniform distribution.


108) Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16

customers per hour. What is the probability that in the next hour there will be exactly 12

arrivals?

108) _____

A) 0.7500

B) 0.0661

C) 0.1322

D) 0.0000


109) Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers

per hour.

What is

the

probabili

ty that in

the next

hour

there

will be

exactly 8

arrivals?

109) ____

_

A) 1.000

B) 0.175

C) 0.825

D) 0.200


110) Which of the following statements concerning the F distribution is true? 110) _____

A) The F distribution is discrete.

B) The F distribution is symmetrical.

C) The F distribution is useful in modeling customer arrivals.

D) The F distribution is interchangeable with the normal distribution for large sample sizes.

E) The F distribution is useful in testing hypotheses about variance.

111) What is the F value associated with α = 0.05, numerator degrees of freedom (df1) equal to 4, and

denominator degrees of freedom (df2) equal to 9?

111) _____

A) 1.80 B) 6.0 C) 0.11 D) 0.18 E) 3.63

112) Which of the following characteristics is not true for the exponential distribution? 112) _____

A) It is used to describe the times between customer arrivals.

B) The variance is the square of the expected value.

C) It is also called the negative exponential distribution.

D) It is used in dealing with queuing problems.

E) It is discrete probability distribution.

113) The length of time that it takes the tollbooth attendant to service each driver can typically be

described by the

113) _____

A) uniform distribution.

B) Poisson distribution.

C) exponential distribution.

D) normal distribution.


114) The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3

per minute) when it comes to license renewals. The service time follows an exponential

distribution. What is the probability that it will take less than 2 minutes for a particular customer

to get a license renewal?

114) _____

A) 0.487 B) 0.1 C) 1 D) 0 E) 0.513

115) The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3

per minute) when it comes to license renewals. The service time follows an exponential

distribution. What is the probability that it will take less than 3 minutes for a particular customer

to

get a

licen

se

renew

al?

115) _____

A) 0.632 B) 0.5 C) 0 D) 1 E) 0.368

116) Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods. The time

between consecutive driver arrivals follows an exponential distribution. What is the probability

that takes less than 1/2 of a minute between consecutive drivers?

116) _____

A) 0.223 B) 0.777 C) 0.167 D) 1 E) 0.5

117) Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods. The time

between consecutive driver arrivals follows an exponential distribution. What is the probability

that takes more than 1/3 of a minute between consecutive drivers?

117) _____

A) 0.632

B) 0.632

C) 0.111

D) 0.368

E) Not enough information given

ESSAY. Write your answer in the space provided or on a separate sheet of paper.

118) An urn contains 7 blue and 3 yellow chips. If the drawing of chips is done with replacement, determine the

probability of:

(a) drawing three yellow chips.

(b) drawing a blue chip on the first draw and a yellow chip on the second draw.

(c) drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw.

(d) drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw.

(e) drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw.

119) A market research study is being conducted to determine if a product modification will be well received by

the public. A total of 1,000 consumers are questioned regarding this product.

The table below provides information regarding this sample.

Positive

Reaction

Neutral

Reaction

Negative

Reaction

Male 240 60 100

Female 260 220 120

(a) What is the probability that a randomly selected male would find this change unfavorable

(negative)?

(b) What is the probability that a randomly selected person would be a female who had a positive

reaction?

(c) If it is known that a person had a negative reaction to the study, what is the probability that the

person is male?

120) In a production run of 300 units, there are exactly 20 defective items and 280 good items.

(a) What is the probability that a randomly selected item is defective?

(b) If two items are sampled without replacement, what is the probability that both are good?

(c) If two items are randomly sampled without replacement, what is the probability that the first is good

but the second is defective?

121) A new television program was viewed by 200 people (120 females and 80 males). Of the females, 60 liked

the program and 60 did not. Of the males, 60 of the 80 liked the program.

(a) What is the probability that a randomly selected individual liked the program?

(b) If a male in this group is selected, what is the probability that he liked the program?

(c) What is the probability that a randomly selected individual is a female and liked the program?

122) Colonel Motors (an automobile company) has prepared a marketing campaign for its best selling car. The

focus of the campaign is quality, and it is claimed that 97 percent of the purchasers of this car have no

complaints in the first year. You and your sister Kim have each purchased one of these cars.

(a) What is the probability that neither of you has a complaint about the car in the first year if the

advertising claim is true?

(b) What is the probability that exactly one of you has a complaint about the car in the first year if the

advertising claim is true?

123) A local "home TV repair service" company has two repairmen who make all of the home repairs. The

company sends Repairman D on 70 percent of all jobs, because the likelihood of a "second follow-up call"

within a week is only 0.08 compared to 0.20 for Repairman K. If you had a recent repair job that is going to

require a second follow-up call, what is the probability that Repairman K did your initial repair work?

124) Our department store is having a sale on personal computers, of which three are in stock (no rain checks).

There is a certain probability of selling none. The probability of selling one is twice as great as the

probability of selling none. The probability of selling two is three times the probability of selling none.

Finally, the probability of selling all the personal computers is four times as great as the probability of selling

none. In a table, list the outcomes and their probabilities. Hint: Let the probability of selling none equal x.

125) ABC Manufacturing has 6 machines that perform a particular task. Breakdowns occur frequently for this

machine. Past records indicate that the number of breakdowns that occur each day is described by the

following probability distribution:

Number of

Breakdowns Probability

0 0.4

1 0.3

2 0.2

3 0.1

More than 3 0.0

(a) What is the expected number of breakdowns in any given day?

(b) What is the variance for this distribution?

(c) What is the probability that there will be at least 2 breakdowns in a day?

126) Fast Service Store has maintained daily sales records on the various size "Cool Drink" sales.

"Cool Drink" Price Number Sold

$0.50 75

$0.75 120

$1.00 125

$1.25 80

Total 400

Assuming that past performance is a good indicator of future sales,

(a) what is the probability of a customer purchasing a $1.00 "Cool Drink?"

(b) what is the probability of a customer purchasing a $1.25 "Cool Drink?"

(c) what is the probability of a customer purchasing a "Cool Drink" that costs greater than or equal to

$1.00?

(d) what is the expected value of a "Cool Drink"?

(e)

what is the variance of a "Cool Drink"?

127) In a given office, the color printer breaks down with a probability of 20% in any month. A binomial process

is assumed for a period of 10 months.

(a) What is the probability that the printer breaks down exactly 2 times?

(b) What is the probability that the printer breaks down at most 1 time?

(c) What is the probability that the printer breaks down more than once?

128) A southwestern tourist city has records indicating that the average daily temperature in the summer is 82

degrees F, which is normally distributed with a standard deviation of 3 degrees F. Based on these records,

determine:

(a) the probability of a daily temperature between 79 degrees F and 85 degrees F.

(b) the probability that the daily temperature exceeds 90 degrees F.

(c) the probability that the daily temperature is below 76 degrees F.

129) Using the table for finding the areas under normal curves, find the area under a normal curve with a mean of

200 and a standard deviation of 10 between the values of:

(a) 200 to 205.

(b) 195 to 205.

(c) 200 to 215.

(d) 195 to 215.

(e) 186.5 to 217.

130) The time required to complete a project is known to be normally distributed with a mean of 44 weeks and a

standard deviation of 8 weeks.

(a) What is the probability that the project is finished in 40 weeks or fewer?

(b) What is the probability that the project is finished in 52 weeks or fewer?

(c) There is an 95 percent chance that the project will be finished in fewer than how many weeks?

131) Compute the F value based on the following:

(a) df1 = 2, df2 = 4, α = 0.01

(b) df1 = 3 df2 = 6, α = 0.05

132) A call center receives calls from customers at a rate of 2 per min. The time between customer calls follows an

exponential distribution.

(a) What is the probability that it takes 1/3 of a minute or less between consecutive customer calls?

(b) What is the probability that it take 1/2 of a minute or more between consecutive customer calls?

133) Arrivals in a university advising office during the week of registration are known to follow a Poisson

distribution with an average of 4 people arriving each hour.

(a) What is the probability that exactly 4 people will arrive in the next hour?

(b) What is the probability that exactly 5 people will arrive in the next hour?

134) Explain why event probabilities range from 0 to 1.

135) Using a standard deck of 52 cards, explain why the situation of drawing a 7 and a club is not collectively

exhaustive.

136) Name five common probability distributions.

137) If two events (A,B) are mutually exclusive, what is the probability of event A or event B occurring?

138) If two events (A,B) are not mutually exclusive, what is the probability of event A or event B occurring?

139) If two events (A,B) are independent, what is their joint probability?

140) If two events (A,B) are dependent, what is the conditional probability of P(A|B)?

141) If two events (A,B) are independent, then the conditional probability of P(A|B) = ________.

142) Explain what a discrete random variable is.

143) The exponential distribution often describes ________.

144) List the two parameters of the normal distribution.

145) In what way is the F distribution often used?

146) List the parameter(s) of the Poisson distribution.

1) FALSE

2) TRUE

3) TRUE

4) TRUE

5) TRUE

6) TRUE

7) TRUE

8) TRUE

9) FALSE

10) TRUE

11) TRUE

12) TRUE

13) FALSE

14) FALSE

15) TRUE

16) TRUE

17) TRUE

18) FALSE

19) FALSE

20) FALSE

21) TRUE

22) TRUE

23) FALSE

24) TRUE

25) FALSE

26) TRUE

27) FALSE

28) TRUE

29) FALSE

30) TRUE

31) TRUE

32) TRUE

33) FALSE

34) TRUE

35) FALSE

36) TRUE

37) FALSE

38) TRUE

39) FALSE

40) TRUE

41) B

42) A

43) E

44) C

45) E

46) C

47) B

48) D

49) E

50) A

51) E

52) B

53) D

54) C

55) C

56) C

57) C

58) E

59) C

60) D

61) B

62) B

63) B

64) A

65) C

66) A

67) E

68) A

69) D

70) A

71) A

72) D

73) D

74) C

75) A

76) D

77) D

78) D

79) B

80) A

81) C

82) B

83) E

84) E

85) D

86) A

87) A

88) B

89) E

90) B

91) C

92) E

93) D

94) C

95) A

96) A

97) D

98) B

99) D

100) C

101) A

102) C

103) D

104) B

105) B

106) C

107) B

108) B

109) E

110) E

111) E

112) E

113) C

114) A

115) A

116) B

117) D

118) (a) 0.027 (b) 0.210 (c) 0.700 (d) 0.300 (e) 0.300

119) (a) 100/400 = 0.25 (b) 260/1000 = 0.260 (c) 100/220 = 0.4545

120) (a) 20/300 = 0.067 (b) (280/300)(279/299) = 0.871 (c) (280/300)(20/299) = 0.062

121) (a) 120/200 = 0.60 (b) 60/80 = 0.75 (c) 60/200 = 0.30

122) (a) 0.97(0.97) = 0.9409 (b) 0.03(0.97) + 0.97(0.03) = 0.0582

123) P(K|2nd) = 0.06/(.06+.056) = 0.517

124) Outcome Probability

Sell 0 0.1

Sell 1 0.2

Sell 2 0.3

Sell 3 0.4

125) (a) expected value = 1.0 (b) variance = 1(.4) + 0(.3) + 1(.2) + 4(.1) = 1.0 (c) P(2 or more) = 0.2 + 0.1 = 0.3

126) (a) 125/400 = 0.3125 (b) 80/400 = 0.20 (c) 205/400 = 0.5125

(d) .5(.1875) + .75(.3) + 1(.3125) + 1.25(.2) = .88125 (e) 0.064

127) (a) P(r=2) = 0.3020 (b) P(r≤1) = 0.3758 (c) P(r>1) = 0.6242

128) (a) P(79<X<85) = 0.68268 (b) P(X>90) = 0.00383 (c) P(X<76) = 0.02275

129) (a) 0.19146 (b) 0.38293 (c) 0.43319 (d) 0.62466 (e) 0.86693

130) (a) 0.30854 (b) 0.84135 (c) 44 + 1.645(8) = 57.16

131) (a) 18 (b) 4.76

132) (a) 0.487 (b) 0.368

133) (a) P(X=4) = 0.1954 (b) P(X=5) = 0.1563

134) The number 0 represents no chance of occurrence, while 1 represents a 100 percent chance of occurrence. Any

number between 0 and 1 represents that particular event's chance of occurrence. Any negative number or number

exceeding 1 has no meaning for an event probability.

135) It is possible to draw other cards that are non-clubs and also not a 7.

136) Answers could vary, but may include: binomial, normal, F, exponential, and Poisson.

137) P(A or B) = P(A) + P(B)

138) P(A or B) = P(A) + P(B) - P(A and B)

139) P(AB) = P(A) × P(B)

140) P(A|B) = P(AB)|P(B)

141) P(A)

142) A discrete random variable has a probability value assigned to each event. These values must be between 0 and 1,

and they must sum to 1.

143) the time required to service a customer

144) mean (μ) and standard deviation (σ)

145) It is helpful in testing hypotheses about variances.

146) the mean and the variance λ

true/false. write 't' if the statement is true and 'f' if ......9) _____ 10) the...

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